Real Component Characteristics
So in school many of you learn that a resistor is just that, and a capacitor and inductors or reactive elements, and it might be mentioned that there are some other parasitics associated with them. I have found that this "glossing" over often leads younger engineers to think of this as an unimportant topic...it really matters more than you think.
Figure 1: Lumped Resistor Model
Resistor
So the resistor lumped model(figure 1) is of far less concern than the others.
Typically the ESL(Equivalent Series Inductance) matters when you place a resistor on a gate of a a transistor and you begin to see some oscillation as shown in the example circuit in Figure 1.a.
This can be due to the LC tank that is produced with the various capacitance's of the transistor itself(Transistor Capacitance's: Collector to Base, Collector to Emitter, and Emitter to Base) modeled in Figure 1.b. Note if you are burning out transistors this can be a good indication of an LC tank creating damaging oscillations by building up heat within your transistor as shown in Figure 1.c below.
Furthermore, this ESL which is commonly not documented in the datasheet for most resistors can lead to odd frequency responses as frequencies increase, but unless you are getting into the GHz ranges it is typically less of an issue.
Figure 1.a: So this is a very simple mockup of a open drain circuit.
Figure 1.b: This is the lumped model of the resistor and the gate source capacitance that is present with all mosfets.
Figure 1c: (Green)Pulse Drive & (Red)Gate Oscillations
Figure 2: Lumped Capacitor Model
Capacitor
So the lumped model of a capacitor(figure 2) is probably the most important out of the trio of basic electronics parts to understand.
R1 is showing a leakage resistance, effectively this just means that there is some large resistance from terminal to terminal on this part that over time will allow any built up charge to "leak" out.
R0 is the most common thing to learn about when talking about parasitic, this is the equivalent series resistance, and is almost always specified on the devices datasheets.
Most commonly it matters when used in power supplies. A useful way to think about this is illustrated in the simple circuit in Figure 3. The ESR effectively acts like a resistor(R1) in series with the capacitor(C1). You want to charge up this capacitor but you lose out on some of the potential charge as it is dissipated as heat in the resistor. So the greater the ESR of the capacitor on a SMPS(switch mode power supply) the greater your losses are and the larger the ripple can be as shown in figure 4.
Figure 3: Super reduced SMPS example circuit
Figure 4: Ripple losses
Figure 5: Non-idealized Capacitor impedance over frequency curve
Another misconception of capacitors is that they "filter" out everything at above their 3dB knee, because of their respective reactance equation:
xC=-j/wc
However this doesn't account for the intrinsic inductance. Figure 5 shows the actual impedance curve of a capacitor. This makes sense because at a certain point the captivate element will reach near 0, and then as frequency continues to climb the parasitic inductance will dominate, and we know that as frequency increases the impedance of an inductor goes up with it as shown in its respective equation:
xL=jwL
This should then explain why on some schematics you see a series of decade valued capacitors in parallel Figure 6. Their curves overlap and expand their effective filter range.
Figure 6: Parallel Decade valued Capacitors
Figure 7: Impedance over Frequency Response of Figure 6 Circuit
Figure 8: Lumped Inductor Model
Inductor
Depending on what you do the lumped model of a coil/inductor may be used all the time or nearly none at all.
L1 & L0 in Figure 8 is the ideal inductance value.
R0 represents equivalent series resistance.
Cp is the parasitic capacitance(changes depending on the case, conductor spacing, etc) and generally plays a major part in the self resonance of the part.
R1 represents the core losses in the coil/inductor.
Now with all of this in hand you would not have a hard time doing whatever circuit analysis you needed. However, acquiring/estimating these values can be less trivial. Generally you purchase parts and therefore are at the mercy of the vendor/manufacturer to provide this information. Even the information you'd need to "estimate" these values. So if you are interested in what that math looks like check out this link. That paper provides the equations and context needed to make such calculations/determinations and spares me from having to create my own demonstrations here.